434 On the Differential Equation of Electrical Flow. 



entirely expended in heating the circuit, and there is no 

 margin for the exhibition of power elsewhere. 



Suppose a line A B to represent (E) the line of effective 

 E.M.F. At the extremity A set off A C 

 as the direction of the line representing 

 the P.D. of the condenser. 



Then, as the condenser contains all 

 the energy that is going to be expended 

 on the circuit and on the aether, from 

 what has been said it is clear that A C 

 must be rather longer than the side of 

 the isosceles triangle ; for, if not, the 

 energy stored will not do more than 

 heat the circuit. If therefore a perpen- 

 dicular be dropped upon A B from C. it will fall at a point 

 nearer B than A. 



Join C B, and, further, draw C D to meet A B produced in 

 D, and so that C D A is an isosceles triangle on A D as base, 

 and therefore CDA = /3. Now CB must be the line repre- 

 senting the resultant of the induced electromotive forces F, 

 and however complicated the case may be this line CB is 

 equivalent to two components C D, D B : of which C D results 

 in no expenditure of power because it is in a phase /3 behind 

 the current, and DB is in phase directly opposed to the 

 current, and therefore resulting in whatever expenditure of 

 energy takes place outside the circuit, and therefore in the 

 aether or in magnetic bodies, or in neighbouring or surround- 

 ing conductors. As in the former case of sustained oscillations, 

 it may be shown that BCD is a magnetic lag necessary for 

 the exhibition of such phenomena. 



The electromotive force DB may be expressed by — \C as 

 before, and the general equation 



v+f=e 



takes the form 



y~L^-\C = RC, 

 at 



and, as this may be written 



V-Lf=(E + X) C) 



we see that the extra consideration required to express the 

 actual state of things is simply that the resistance of the 

 circuit is virtually increased. In the previous work it is 

 necessary to write (R + X) in all the equations. 



